Generators (Parallel-Coordinate Plots (PCP))¶
Notebook for generating basic PCPs of the Pareto-optimal fronts with appropriate colorings and point-sizes.¶
This notebook can be used to generate basic PCPs of all the Pareto-optimal fronts with suitable colorings and point-sizes. This notebook tests the plot() fucntion from the vis.plotting.pcp module. All the Pareto-optimal data point files hard-coded in the dictionary pfs. Currently this notebook provides these Pareto-optimal fronts.
- DTLZ2 ($m$-Sphere) Problem
- DEBMDK (Knee) Problem
- CDEBMDK (Constrained Knee) Problem
- C0-DTLZ2 (A split $m$-sphere with a small isolated cluster at $f_m$-axis)
- C2-DTLZ2 Problem
- DTLZ8 Problem (A 3-dimensional line and an $m$-dimensional hypersurface)
- GAA Problem (A 10-objective and 18-constraint general aviation design problem)
In [1]:
%reload_ext autoreload
%autoreload 2
import sys
import os
import numpy as np
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import Axes3D
plt.rcParams.update({'figure.max_open_warning': 0})
Generate and save plots.¶
In [2]:
sys.path.append('../')
from vis.plotting.utils import resize_by_tradeoff, color_by_dist, color_by_cv, enhance_color
def load_props(path):
r"""
Load CV, Mu, Ik and S from path.
"""
CV = None
cvpathf = os.path.join(path, "datacv.csv")
if os.path.exists(cvpathf):
CV = np.loadtxt(cvpathf)
# load the Mu values
Mu = None
mupathf = os.path.join(path, "mu.csv")
if os.path.exists(mupathf):
Mu = np.loadtxt(mupathf)
# load the knee indices
Ik = None
kpathf = os.path.join(path, "muid.csv")
if os.path.exists(kpathf):
Ik = np.loadtxt(kpathf, dtype=int)
return CV, Mu, Ik
def decide_size_color(CV, Mu, Ik):
r"""
Decide point-size and color from `CV`, `Mu` and `Ik`
"""
# decide point-size
S = 1
if Mu is not None and Ik is not None:
S = resize_by_tradeoff(Mu, k=Ik)
# decide colors
# C = default_color(F.shape[0], alpha=0.5)
M = np.mean(F, axis=0)
C, D = color_by_dist(F, M, alpha=0.15)
# if CV is available, use CV to color
if CV is not None:
C = color_by_cv(CV, alpha=0.15)
# enhance knee points
if Ik is not None:
C = enhance_color(C, Ik, alpha=0.5)
return S, C, D
Do PCPs¶
In [3]:
%matplotlib inline
sys.path.append('../')
from vis.plotting import pcp
from vis.utils import transform as tr
pfs = {'dtlz2': ['3d', '4d', '8d'], \
'dtlz2-nbi': ['3d', '4d', '8d'], \
'debmdk': ['3d', '4d', '8d'], \
'debmdk-nbi': ['3d', '4d', '8d'], \
'debmdk-all': ['3d', '4d', '8d'], \
'debmdk-all-nbi': ['3d', '4d', '8d'], \
'dtlz8': ['3d', '4d', '6d', '8d'], \
'dtlz8-nbi': ['3d', '4d', '6d', '8d'], \
'c2dtlz2': ['3d', '4d', '5d', '8d'], \
'c2dtlz2-nbi': ['3d', '4d', '5d', '8d'], \
'cdebmdk': ['3d', '4d', '8d'], \
'cdebmdk-nbi': ['3d', '4d', '8d'], \
'c0dtlz2': ['3d', '4d', '8d'], \
'c0dtlz2-nbi': ['3d', '4d', '8d'], \
'crash-nbi': ['3d'], 'crash-c1-nbi': ['3d'], 'crash-c2-nbi': ['3d'], \
'gaa': ['10d'], \
'gaa-nbi': ['10d']}
constrained_pfs = ['dtlz8', 'dtlz8-nbi', \
'c2dtlz2', 'c2dtlz2-nbi', \
'cdebmdk', 'cdebmdk-nbi', \
'c0dtlz2', 'c0dtlz2-nbi', \
'gaa', 'gaa-nbi']
for pf in list(pfs.keys()):
for dim in pfs[pf]:
fullpathf = "../data/{0:s}/{1:s}/dataf.csv".format(pf, dim)
if os.path.exists(fullpathf):
path, filenamef = os.path.split(fullpathf)
dirs = path.split('/')
frontname = dirs[-2]
# load the front
F = np.loadtxt(fullpathf, delimiter=',')
# we need to normalize in the case of pcp, otherwise the data will not be
# visible in some cases.
F = tr.normalize(F, lb = np.zeros(F.shape[1]), ub = np.ones(F.shape[1]))
print(fullpathf, F.shape, dirs, frontname)
# decide on colors and sizes
CV, Mu, Ik = load_props(path)
S,C,D = decide_size_color(CV, Mu, Ik)
# all indices
I = np.arange(0,F.shape[0],1).astype(int)
# indices of non-knee points
Ip = np.setdiff1d(I, Ik)
# non-knee points
Fp = F[Ip,:]
Cp = C[Ip,:]
# xtick_labels
Lt = np.array(["$f_{{{:d}}}$".format(v) for v in range(Fp.shape[1])])
# line labels
Llp = np.array(["All other points".format(v) for v in range(Ip.shape[0])])
# knee colors
Ck = C[Ik,:]
# knee point line labels
Llk = np.array(["Knee points".format(v) for v in range(Ik.shape[0])])
# get distnace from centroid or cv values
Dp = CV[Ip] if pf in constrained_pfs else D[Ip]
# sort the points and their colors w.r.t. distance from centroid or cv, i.e. Dp
Id = np.column_stack((Dp, Fp, Cp)).astype(object)
Id = Id[np.argsort(Id[:, 0])]
if pf in constrained_pfs:
# points are sorted ascendingly w.r.t Dp and they will be plotted according
# to that order, therefore, we reverse them so that the points closer to the
# constraint boundaries (pink points) will be plotted last.
Fp = Id[:,1:Fp.shape[1]+1].astype(float)
Cp = Id[:,Fp.shape[1]+1:].astype(float)
# since we are not plotting in a reverse order,
# we don't need to flip the color bar
cbar_flip = False
cbar_label = "Cumulative normalized CV"
else:
# points are sorted ascendingly w.r.t Dp and they will be plotted according
# to that order, therefore, we reverse them so that the points closer to the
# centroid (light-green points) will be plotted last.
Fp = Id[:,1:Fp.shape[1]+1].astype(float)[::-1]
Cp = Id[:,Fp.shape[1]+1:].astype(float)[::-1]
# since we are plotting in a reverse order,
# we need to flip the color bar
cbar_flip = True
cbar_label = "Centroid distance"
# the colorbar gradient will be according to Dp
Cgp = Dp
figpath = os.path.join(path, "pcp.pdf")
with plt.rc_context({"text.usetex": True, "font.size": 12}):
ax = plt.figure().gca()
# plot non-knee points
pcp.plot(Fp, ax=ax, c=Cp, lw=1.00, xtick_labels=Lt, line_labels=Llp, show_colorbar=True, \
cbar_grad=Cgp, cbar_label=cbar_label, cbar_flip=cbar_flip)
# plot knee points
pcp.plot(F[Ik,:], ax=ax, c=Ck, lw=1.50, line_labels=Llk)
# save the fig
plt.savefig(figpath, bbox_inches='tight', dpi=150, pad_inches=0)
# show
plt.show()
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